U.S. patent application number 15/071354 was filed with the patent office on 2016-10-13 for pulsatile perfusion bioreactor for mimicking, controlling, and optimizing blood vessel mechanics.
The applicant listed for this patent is University of South Carolina. Invention is credited to John F. Eberth, Conrad Michael Gore, David A. Prim, Tarek Shazly, Boran Zhou.
Application Number | 20160298073 15/071354 |
Document ID | / |
Family ID | 57111278 |
Filed Date | 2016-10-13 |
United States Patent
Application |
20160298073 |
Kind Code |
A1 |
Eberth; John F. ; et
al. |
October 13, 2016 |
Pulsatile Perfusion Bioreactor for Mimicking, Controlling, and
Optimizing Blood Vessel Mechanics
Abstract
A pulsatile perfusion bioreactor for culturing one or more
engineered blood vessels having a lumen and a wall is provided. The
bioreactor includes a chamber for holding the engineered blood
vessel and cell culture media; a mechanical property monitoring
system for measuring axial tensile stress and strain,
circumferential tensile stress and strain, and/or shear stress
imparted on the vessel wall; and a pump system for delivering cell
culture media through the vessel lumen, wherein the vessel is
exposed to a composite pressure waveform and a composite flow
waveform as the media is delivered there through. The pump system
includes a steady flow and peristaltic pumps. Further, the
composite pressure and flow waveforms each include a mean
component, a fundamental frequency component, and a second harmonic
frequency component. The bioreactor also includes a computer
interface for monitoring and adjusting the composite waveforms to
maintain a predetermined stress levels.
Inventors: |
Eberth; John F.; (Columbia,
SC) ; Shazly; Tarek; (Columbia, SC) ; Zhou;
Boran; (Columbia, SC) ; Prim; David A.;
(Columbia, SC) ; Gore; Conrad Michael; (West
Columbia, SC) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
University of South Carolina |
Columbia |
SC |
US |
|
|
Family ID: |
57111278 |
Appl. No.: |
15/071354 |
Filed: |
March 16, 2016 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62143844 |
Apr 7, 2015 |
|
|
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
C12M 29/12 20130101;
C12M 21/08 20130101; C12M 29/00 20130101; C12M 35/04 20130101; C12M
29/10 20130101; C12M 41/40 20130101; C12N 5/0691 20130101; C12M
25/10 20130101 |
International
Class: |
C12M 1/00 20060101
C12M001/00; C12N 5/071 20060101 C12N005/071; C12M 1/34 20060101
C12M001/34 |
Claims
1. A pulsatile perfusion bioreactor for culturing one or more
engineered blood vessels having a lumen and a wall, the pulsatile
perfusion bioreactor comprising: a chamber for holding the
engineered blood vessel and cell culture media; a mechanical
property monitoring system for measuring and controlling axial
tensile stress, circumferential tensile stress, shear stress, or a
combination thereof imparted on the wall of the engineered blood
vessel and for measuring and controlling axial stretch,
circumferential stretch, or a combination thereof imparted on the
wall of the engineered blood vessel; a pump system for delivering
cell culture media through the lumen of the engineered blood
vessel, wherein the engineered blood vessel is exposed to a
composite pressure waveform and a composite flow waveform as the
cell culture media is delivered through the lumen, the pump system
comprising a steady flow pump and a peristaltic pump, wherein the
composite pressure waveform comprises a mean pressure component, a
first harmonic frequency pressure component, and a second harmonic
frequency pressure component, and wherein the composite flow
waveform component comprises a mean flow component, a first
harmonic frequency flow component, and a second harmonic frequency
flow component; and a computer interface for monitoring and
adjusting the composite pressure waveform, the composite flow
waveform, or a combination thereof to maintain a predetermined
axial tensile stress level, a predetermined circumferential stress
level, a predetermined shear stress level, or a combination
thereof.
2. The bioreactor as in claim 1, wherein the composite pressure
waveform and the composite flow waveform are derived from a
pressure waveform and a flow waveform of a native blood vessel,
wherein the engineered blood vessel is a replacement for the native
blood vessel.
3. The bioreactor as in claim 1, wherein the steady flow pump
delivers the mean pressure component of the composite pressure
waveform and the mean flow component of the composite flow
waveform.
4. The bioreactor as in claim 1, wherein the peristaltic pump
delivers a pulsatile flow of cell culture media through the lumen,
wherein the peristaltic pump comprises a first pump head and a
second pump head, wherein the first pump head provides the first
harmonic frequency pressure component of the composite pressure
waveform and the first harmonic frequency flow component of the
composite flow waveform, and wherein the second pump head provides
the second harmonic frequency pressure component of the composite
pressure waveform and the second harmonic frequency flow component
of the composite flow waveform.
5. The bioreactor as in claim 4, wherein the peristaltic pump
further comprises a third pump head, wherein the third pump head
provides a third harmonic frequency pressure component of the
composite pressure waveform and a third harmonic frequency flow
component of the composite flow waveform.
6. The bioreactor as in claim 1, further comprising a compliance
chamber.
7. The bioreactor as in claim 1, further comprising a pressure
transducer.
8. The bioreactor as in claim 1, further comprising a stepper motor
controlled pinch valve.
9. The bioreactor as in claim 1, further comprising a camera for
measuring the engineered blood vessel length, wall diameter, and
wall thickness.
10. The bioreactor as in claim 1, wherein the chamber is located in
an incubator.
11. The bioreactor as in claim 1, wherein the engineered blood
vessel comprises a natural material or a synthetic material.
12. The bioreactor as in claim 1, wherein the engineered blood
vessel includes endothelial cells.
13. The bioreactor as in claim 1, wherein the engineered blood
vessel includes smooth muscle cells.
14. A method of culturing a one or more engineered blood vessels
having a lumen and a wall inside a pulsatile perfusion bioreactor,
the method comprising: inserting the engineered blood vessel to be
cultured into a chamber; filling the chamber with cell culture
media; delivering cell culture media through the lumen of the
engineered blood vessel via a pump system, wherein the engineered
blood vessel is exposed to a composite pressure waveform and a
composite flow waveform as the cell culture media is delivered
through the lumen, the pump system comprising a steady flow pump
and a peristaltic pump, wherein the composite pressure waveform
comprises a mean pressure component, a first harmonic frequency
pressure component, and a second harmonic frequency pressure
component, and wherein the composite flow waveform component
comprises a mean flow component, a first harmonic frequency flow
component, and a second harmonic frequency flow component;
measuring axial tensile stress, circumferential tensile stress,
shear stress, axial stretch, circumferential stretch, or a
combination thereof imparted on the wall of the engineered blood
vessel via a mechanical property monitoring system; monitoring and
adjusting the composite pressure waveform, the composite flow
waveform, or a combination thereof to maintain a predetermined
axial tensile stress level, a predetermined circumferential stress
level, a predetermined shear stress level, a predetermined axial
stretch level, a predetermined circumferential stretch level, or a
combination thereof via a computer interface.
15. The method as in claim 14, wherein the composite pressure
waveform and the composite flow waveform are derived from a
pressure waveform and a flow waveform of a native blood vessel,
wherein the engineered blood vessel is a replacement for the native
blood vessel.
16. The method as in claim 14, wherein the steady flow pump
delivers the mean pressure component of the composite pressure
waveform and the mean flow component of the composite flow
waveform.
17. The method as in claim 14, wherein the peristaltic pump
delivers a pulsatile flow of cell culture media through the lumen,
wherein the peristaltic pump comprises a first pump head and a
second pump head, wherein the first pump head provides the first
harmonic frequency pressure component of the composite pressure
waveform and the first harmonic frequency flow component of the
composite flow waveform, and wherein the second pump head provides
the second harmonic frequency pressure component of the composite
pressure waveform and the second harmonic frequency flow component
of the composite flow waveform.
18. The method as in any of claim 17, wherein the peristaltic pump
further comprises a third pump head, wherein the third pump head
provides a third harmonic frequency pressure component of the
composite pressure waveform and a third harmonic frequency flow
component of the composite flow waveform.
19. The method as in claim 15, wherein the pulsatile perfusion
bioreactor includes a compliance chamber, wherein the compliance
chamber facilitates adjustment of the composite pressure
waveform.
20. The method as in claim 15, wherein pressure is measured via a
pressure transducer and a stepper motor controlled pinch valve is
utilized to adjust resistance within the pulsatile perfusion
bioreactor, wherein adjusting the resistance results in an
adjustment to the pressure.
Description
RELATED APPLICATIONS
[0001] The present application claims priority to U.S. Provisional
Application Ser. No. 62/143,844, filed on Apr. 7, 2015, which is
incorporated herein in its entirety by reference thereto.
BACKGROUND
[0002] The field of vascular tissue engineering seeks to generate
functional blood vessels with properties similar to that of healthy
tissue. Engineered tissues may originate from biocompatible
scaffolds embedded with diverse populations of cells or through
altering existing tissues exposed to controlled stimulation that
initiate known intrinsic adaptive processes. The demand for such
functional tissues is especially great in the vascular system,
where engineered blood vessels (EBVs) could be used to replace
diseased or damaged blood vessels in patients suffering from
advanced stage atherosclerosis or other focalized degenerative
diseases. For example, nearly 400,000 coronary artery bypass grafts
and around 50,000 peripheral vascular grafts were performed in the
United States each year. However, patients often lack viable
autograft tissue and purely synthetic replacements (e.g.,
DACRON.RTM. grafts) become occluded when used to replace small
diameter vessels. As such, there is a need for the development of
functional EBVs that are biocompatible, are anti-thrombogenic, and
that exhibit autograft-like levels of burst and fatigue strength.
Accordingly, various approaches have been employed over the years
to engineer blood vessels that meet these requirements, yet few
have reached advanced stage clinical trials. Therefore the
practical and commercial development of this technology remains an
emerging field.
[0003] In the development of EBVs, the choice of scaffold material,
cell type, and assembly are typically considered. The mechanical
environment and the bioreactor utilized for culturing the EBV must
also be considered. The mechanical environment includes the biaxial
stresses and stretches generated in the circumferential and the
axial directions of the EBV, as well as the fluid-induced wall
shear stresses focused along the endothelial cell (EC) lined lumen
of the EBV. In vivo, the circumferential loading is a result of
pressurization and the axial loading is a result of somatic growth.
It has also been observed that natural tissues seek to restore
levels of mechanical stress. For example, in sustained
hypertension, which elicits an acute increase in circumferential
wall stress, the primary remodeling outcome is an increase in wall
thickness, which in turn acts to restore the wall stress to
baseline, or normotensive, stress levels. Accordingly, the
mechanical environment has been identified as a major contributor
to the growth and remodeling of a biomimetic EBV and is an
important physical factor in vascular graft generation and
homeostasis. Specifically, cyclic stretching of intramural vascular
cells initiates proliferation, promotes the release of growth
factors, alters fiber realignment, regulates smooth muscle cell
(SMC) contractile phenotype, and encourages overall extracellular
matrix (ECM) synthesis (e.g., collagen, tropoelastin, etc.) and
tissue turnover by SMCs and fibroblasts. Similarly, the frequency,
direction, and magnitude of shear stress on ECs governs metabolic
activities, nutrient exchange, cellular morphology, stress fiber
alignment, and SMC phenotype, and also control paracrine factors
including nitric oxide release, which is a major mediator of
remodeling and homeostasis.
[0004] Over the last fifty years, vascular perfusion bioreactors
have been developed primarily as research tools but have recently
become available in the commercial market. However, commercially
available bioreactors are not designed to implement the
comprehensive mechanical objectives discussed above that are needed
to create a truly biomimetic EBV. As such, a need exists for a EBV
bioreactor that has the capability to optimize mechanical (stress)
objectives, which would, in turn, minimize culture time and
maximize output. Furthermore, a need exists for a bioreactor
specific for culturing EBVs that can impose and test biaxial loads,
can deliver specific biomimetic pressure and flow profiles, can be
scalable for different vessels and animals, and can provide for
real time data collection and assessment. A need also exists for a
bioreactor that can be autoclaved, maintain sterility for prolonged
culture times, promote nutrient and gas exchange, actively maintain
temperature and pH, permit cell seeding, and allow for chemical
stimulation and assessment. Such a device could be used in the
commercial setting and not solely as a research tool.
[0005] Moreover, the ultimate success of an EBV lies in its ability
to perform in the intended environment. The biomimetic hemodynamic
loads on the EBV are unique amongst species and anatomical
location, thus the knowledge and application of vessel-specific
hemodynamics and axial loading that mimic the intended graft
condition are both crucial during tissue development in order to
avoid hemodynamically-induced pathologies. As such, a need exists
for a bioreactor that could prescribe dynamic pressure and flow
waveforms during culture that incorporate complex phasic
relationships that are not static or simply sinusoidal. In other
words, a need exists for a bioreactor that can deliver variable
stresses to an engineered blood vessel through the application and
control of dynamic pressure and flow waveforms so that the
engineered blood vessel can be conditioned and remodeled during
ex-vivo culture so that it ultimately possesses properties that
mimic a native blood vessel.
SUMMARY OF THE INVENTION
[0006] The present invention is directed to a pulsatile perfusion
bioreactor for culturing one or more engineered blood vessels
having a lumen and a wall. This invention also provides
mechanomimetic stimulation to the blood vessels and can be used to
study physiological dependent vascular processes such as the
response to endovascular interventions and pharmaceutical
administration. The pulsatile perfusion bioreactor includes one or
more chambers for holding the engineered blood vessel and cell
culture media; a mechanical property monitoring system for
measuring axial tensile stress, circumferential tensile stress,
shear stress, or a combination thereof imparted on the wall of the
engineered blood vessel and for measuring and controlling axial
stretch, circumferential stretch, or a combination thereof imparted
on the wall of the engineered blood vessel; and a pump system for
delivering cell culture media through the lumen of the engineered
blood vessel. The pump system includes a steady flow pump and a
peristaltic pump such that when cultured inside the pulsatile
perfusion bioreactor, the engineered blood vessels are exposed to a
composite pressure waveform and a composite flow waveform as the
cell culture media is delivered through the lumen. The composite
pressure waveform comprises a mean pressure component, a
fundamental frequency (or first harmonic) pressure component and a
second harmonic frequency pressure component, while the composite
flow waveform component comprises a mean flow component, a
fundamental frequency (or first harmonic) flow component and a
second harmonic frequency flow component. However, it is to be
understood that additional harmonic flow frequencies can be added
to improve resolution. The pulsatile perfusion bioreactor further
includes a computer interface for monitoring and adjusting the
composite pressure waveform, the composite flow waveform, or a
combination thereof to maintain a predetermined axial tensile
stress level, a predetermined circumferential stress level, a
predetermined shear stress level, or a combination thereof.
[0007] In an additional embodiment, the composite pressure waveform
and the composite flow waveform can be derived from a pressure
waveform and a flow waveform of a native blood vessel, and the
engineered blood vessel can be a replacement for the native blood
vessel.
[0008] In another embodiment, the steady flow pump can deliver the
mean pressure component of the composite pressure waveform and the
mean flow component of the composite flow waveform. In still
another embodiment, the peristaltic pump can deliver a pulsatile
flow of cell culture media through the lumen via a first pump head
and a second pump head. For example, the first pump head can
provide the fundamental frequency pressure component of the
composite pressure waveform and the fundamental frequency flow
component of the composite flow waveform, while the second pump
head can provide the second harmonic frequency pressure component
of the composite pressure waveform and the second harmonic
frequency flow component of the composite flow waveform. In a
further embodiment, the peristaltic pump can also include a third
pump head, where the third pump head can provide a third harmonic
frequency pressure component of the composite pressure waveform and
a third harmonic frequency flow component of the composite flow
waveform.
[0009] In yet another embodiment, the bioreactor can also include a
compliance chamber. In one more embodiment, the bioreactor can
include a pressure transducer. In an additional embodiment, the
bioreactor can also include a stepper motor controlled pinch valve.
In one particular embodiment, the bioreactor can also include a
camera for measuring the engineered blood vessel length, wall
diameter, wall thickness, or a combination thereof.
[0010] In one embodiment, the bioreactor chamber can be located in
an incubator. Further, the engineered blood vessel can include a
natural material or a synthetic material. Moreover, the engineered
blood vessel can include endothelial cells, smooth muscle cells, or
a combination thereof.
[0011] In yet another embodiment, the present invention is directed
to a method of culturing one or more engineered blood vessels
having a lumen and a wall inside a pulsatile perfusion bioreactor.
The method includes inserting the engineered blood vessel to be
cultured into a chamber; filling the chamber with cell culture
media; delivering cell culture media through the lumen of the
engineered blood vessel via a pump system, wherein the engineered
blood vessel is exposed to a composite pressure waveform and a
composite flow waveform as the cell culture media is delivered
through the lumen, the pump system comprising a steady flow pump
and a peristaltic pump, wherein the composite pressure waveform
comprises a mean pressure component, a fundamental frequency
pressure component and a second harmonic frequency pressure
component, and wherein the composite flow waveform component
comprises a mean flow component, a fundamental frequency flow
component, and a second harmonic frequency flow component;
measuring axial tensile stress, circumferential tensile stress,
shear stress, axial stretch, circumferential stretch, or a
combination thereof imparted on the wall of the engineered blood
vessel via a mechanical property monitoring system; and monitoring
and adjusting the composite pressure waveform, the composite flow
waveform, or a combination thereof to maintain a predetermined
axial tensile stress level, a predetermined circumferential stress
level, a predetermined shear stress level, a predetermined axial
stretch level, a predetermined circumferential stretch level, or a
combination thereof via a computer interface.
[0012] In an additional embodiment, the composite pressure waveform
and the composite flow waveform can be derived from a pressure
waveform and a flow waveform of a native blood vessel, and the
engineered blood vessel can be a replacement for the native blood
vessel.
[0013] In another embodiment, the steady flow pump can deliver the
mean pressure component of the composite pressure waveform and the
mean flow component of the composite flow waveform.
[0014] In still another embodiment, the peristaltic pump can
deliver a pulsatile flow of cell culture media through the lumen.
The peristaltic pump can include a first pump head and a second
pump head, where the first pump head can provide the fundamental
frequency pressure component of the composite pressure waveform and
the fundamental frequency flow component of the composite flow
waveform, while the second pump head can provide the second
harmonic frequency pressure component of the composite pressure
waveform and the second harmonic frequency flow component of the
composite flow waveform.
[0015] In yet another embodiment, the peristaltic pump can further
include a third pump head, where the third pump head provides a
third harmonic frequency pressure component of the composite
pressure waveform and a third harmonic frequency flow component of
the composite flow waveform.
[0016] In an additional embodiment, the pulsatile perfusion
bioreactor can include a compliance chamber, where the compliance
chamber can facilitate adjustment of the composite pressure
waveform and can reduce noise caused by the peristaltic pump. In
still another embodiment, pressure can be measured via a pressure
transducer and a stepper motor controlled pinch valve can be
utilized to adjust resistance within the pulsatile perfusion
bioreactor, wherein adjusting the resistance results in an
adjustment to the pressure.
[0017] Other features and aspects of the present invention are set
forth in greater detail below.
BRIEF DESCRIPTION OF THE DRAWINGS
[0018] A full and enabling disclosure of the present invention,
including the best mode thereof to one skilled in the art, is set
forth more particularly in the remainder of the specification,
which includes reference to the accompanying figures.
[0019] FIG. 1 shows an example of the physiological blood pressure
(P) and flow (Q) waveforms that can be created an applied to an EBV
via the pulsatile perfusion bioreactor of the present invention.
This example mimics the conditions of a human radial artery.
[0020] FIG. 2 shows a schematic of one embodiment of the pulsatile
perfusion bioreactor of the present invention.
[0021] FIG. 3a shows a porcine renal artery cultured for 10 days in
the pulsatile perfusion bioreactor of the present invention prior
to administration of phenylephrine to elicit smooth muscle cell
(SMC) contraction.
[0022] FIG. 3b shows a porcine renal artery cultured for 10 days in
the pulsatile perfusion bioreactor of the present invention after
administration of phenylephrine to elicit smooth muscle cell (SMC)
contraction.
[0023] FIG. 4 shows the 4-element Windkessel model as an
electro-hydraulic analogy with two resistors, an inductor, and a
capacitor, where the location of the blood vessel for culturing is
marked with an (x).
[0024] FIG. 5a shows the composite hemodynamic pressure waveform
(dotted line) and the mean hemodynamic pressure waveform (n=0;
solid line), as well as the fundamental frequency (or first
harmonic frequency) component (n=1, open circle waveform), and two
harmonic frequency components (n=2, open square waveform and n=3,
open diamond waveform) of the composite hemodynamic pressure
waveform, from a pig renal artery.
[0025] FIG. 5b shows the composite hemodynamic flow waveform
(dotted line) and the mean hemodynamic flow waveform (n=0; solid
line), as well as the fundamental frequency (or first harmonic
frequency) component (n=1, open circle waveform), and two harmonic
frequency components (n=2, open square waveform and n=3, open
diamond waveform) of the composite hemodynamic flow waveform, from
a pig renal artery.
[0026] FIGS. 6a-6c show the velocity profiles (3D map) and measured
centerline velocity (dotted line) for (a) a Human Radial Artery,
(b) a Pig Renal Artery, (c) and a Mouse Aorta.
[0027] FIGS. 7a-7c show the mean (solid flat line) and pulsatile
(solid parabolic/sinusoidal line) wall shear stress (.tau..sub.w,)
for (a) a Human Radial Artery, (b) a Pig Renal Artery, and (c) a
Mouse Aorta.
[0028] FIGS. 8a-8c show the desired (solid line) and simulated
(open circles) pressure responses using the best fit parameters of
the electro-hydraulic 4-element Windkessel model. The desired
pressure is reported in the literature for (a) a Human Radial
Artery, (b) a Pig Renal Artery, (c) and a Mouse Aorta which also
shows a zoomed-in section on one mouse cardiac cycle.
[0029] Repeat use of reference characters in the present
specification and drawings is intended to represent the same or
analogous features or elements of the present invention.
DETAILED DESCRIPTION
[0030] Reference now will be made to the embodiments of the
invention, one or more examples of which are set forth below. Each
example is provided by way of an explanation of the invention, not
as a limitation of the invention. In fact, it will be apparent to
those skilled in the art that various modifications and variations
can be made in the invention without departing from the scope or
spirit of the invention. For instance, features illustrated or
described as one embodiment can be used on another embodiment to
yield still a further embodiment. Thus, it is intended that the
present invention cover such modifications and variations as come
within the scope of the appended claims and their equivalents. It
is to be understood by one of ordinary skill in the art that the
present discussion is a description of exemplary embodiments only,
and is not intended as limiting the broader aspects of the present
invention, which broader aspects are embodied exemplary
constructions.
[0031] It is understood that mechanical signals are key mediators
of the cellular processes which underlie blood vessel remodeling,
including proliferation, differentiation, migration, and protein
synthesis. Further, blood vessels are dynamic in form, function,
and pulsatility (i.e., the difference between the maximum and
minimum blood pressure and flow). Blood pressure induces periodic
circumferential stresses, which are sensed by smooth muscle cells
and fibroblasts embedded in the vascular wall, whereas blood flow
induces periodic and often oscillatory wall shear stresses, which
are sensed by endothelial cells lining the lumen. In addition, it
has been shown that the production of extracellular matrix material
and the alignment of smooth muscle cells and fibroblasts both
depend on the rate and magnitude of cyclic stretching. Furthermore,
gene profiles of endothelial cells in culture are dependent upon
the magnitude and frequency of flow oscillation with a morphology
that discriminates between different flow environments. Vascular
pathologies also depend on the cyclic and oscillatory flow such as
those observed in atherosclerosis formation. Thus, blood vessel
growth and remodeling are highly dependent on the pressure and flow
waveforms and stresses to which the blood vessel is exposed. As
such, an accurate means of applying pressure and flow waveforms to
a EBV and adjusting the pressure and flow waveforms to achieve
desired stress and loading objectives is important in obtaining a
truly biomimetic EBV and can be accomplished via the pulsatile
perfusion bioreactor of the present invention.
[0032] Meanwhile, although in-vivo and ex-vivo experimental studies
have been conducted to delineate remodeling outcomes under
prescribed loading conditions, with a manifest dependence on
vascular wall stresses, no ex-vivo culture systems are available
that can accurately translate remodeling principles (i.e.,
stress-driven growth) into the development of commercially
available EBVs, where the amount of stress applied to the EBV can
be accurately controlled during culturing so that the engineered
blood vessel is exposed to stresses equivalent to those to which a
native blood vessel is exposed. This is due, in part, to the
complexity of conferring biomimetic pulsatile loading in a
three-dimensional tissue culture environment that integrates both
the fluid and solid domains, the challenges of retaining tissue
viability for extended culture periods, and the wide variation in
the types and sizes of EBVs to be cultured. Furthermore, stress
levels imparted to an EBV must be tightly controlled throughout
culture, as exceeding material and maturation state-specific stress
thresholds can lead to material failure or potentially adverse
cellular responses (i.e., apoptosis). To solve this problem, the
pulsatile perfusion bioreactor of the present invention can
accurately replicate the pressure and flow waveforms of the native
vessel that the EBV is intended to replace and can make real time
adjustments to the waveforms as the EBV is cultured to maintain
desired stress levels. As such, the present inventors have found
that an EBV cultured in the pulsatile perfusion bioreactor of the
present invention can undergo remodeled during culture so that the
end product mimics the native vessel it is to replace.
[0033] As discussed in more detail below, the present inventors
have developed an ex-vivo pulsatile perfusion bioreactor that
enables for the control of mechanically-induced tissue growth and
remodeling of an EBV that closely mimics in vivo conditions via the
application of specified stress levels through the control of
pressure and flow waveforms applied to the EBV in culture. In other
words, the pulsatile perfusion bioreactor of the present invention
can control deterministic aspects of blood vessel mechanics and can
facilitate functional vascular tissue remodeling in engineered
blood vessels having a synthetic or biological origin. For
instance, through application of biomimetic pressure and flow
waveforms and real-time assessment of sample geometry and
mechanical properties, the pulsatile perfusion bioreactor of the
present invention enables the control and optimization of culture
conditions for various sizes and types of engineered vascular
tissues formed from both natural and synthetic materials. Further,
the pulsatile perfusion bioreactor of the present invention allows
for collection of sample data using a computer interface with
minimal human intervention, thus mitigating contamination potential
and enabling a feedback control system for optimizing vascular
tissue growth. Dynamic flow-induced wall shear stress and
three-dimensional tensile wall stress conditions can be controlled
and adjusted to predetermined objective values based on the type of
native blood vessel being replaced with the EBV, and flow/pressure
profiles and imposed axial stretch can be tuned and adjusted during
culture to maintain the predetermined objective values, resulting
in a EBV having properties that mimic those of the native blood
vessel that it will replace. Furthermore, the mechanical
suitability of EBV can be tested directly within the pulsatile
perfusion bioreactor of the present invention, which can streamline
the iterative refinement of culture protocol that is implicit in
the development of any tissue-engineered product.
[0034] In addition, while currently available bioreactors enable
specification of the global mechanical environment of vascular
tissue samples (e.g., lumen pressure, flow rate, and axial
extension), the pulsatile perfusion bioreactor of the present
invention additionally allows for specification of the local
mechanical environment of resident vascular cells (e.g., wall
tensile stresses (circumferential and axial) and flow-induced shear
stress). This is a critical distinction, as the local mechanical
environment changes as the vessel remodels and is what drives
mechanosensitive cellular processes. The pulsatile perfusion
bioreactor of the present invention can thus consistently impart
biomimetic stresses to the EBV being cultured, and that tissue
viability and function can be retained at least over a two-week
culture period. Irrespective of the particular application, the
pulsatile perfusion bioreactor of the present invention is
configured to allow for the automated control of fundamental
mechanical signals governing vascular tissue remodeling. The
driving mechanical stimuli for native vascular tissue growth and
remodeling are wall stresses operative at the intima (e.g.,
flow-induced shear stress, which is sensed and regulated by
vascular endothelial cells) and within the media (e.g., tensile
stress in the axial and circumferential directions, which is sensed
and regulated by vascular smooth muscle cells) of a blood vessel.
Thus, the ability to control these same mechanical quantities in a
bioreactor can elicit control of growth and remodeling processes in
cell-laden EBVs. In order to promote the cellular processes
implicit in vascular tissue generation, it is critical that imposed
stresses are derived from biomimetic mechanical loading profiles
(i.e., physiological pressure and flow waveforms). The application
of biomimetic mechanical loading on the EBV culture in the
pulsatile perfusion bioreactor of the present invention via the
application of pressure and flow waveforms that mimic physiological
pressure and flow waveforms can thus create an ex-vivo environment
in which vascular cell behavior can be understood, predicted, and
ultimately directed towards functional engineered tissue
generation.
[0035] As mentioned above, currently available bioreactor systems
feature control of the lumen pressure, flow rate, and in some cases
the degree of axial stretch to which samples are subjected, (i.e.,
control of the global mechanical loading). Further, such
bioreactors utilize pressure and flow waveforms that are gross
approximations of physiologic loading (e.g., sine waves or steady
flows) such that the resulting mechanical environment in which an
EBV is cultured substantially deviates from that of native vessels.
In contrast, the pulsatile perfusion bioreactor of the present
invention allows for user control of the wall stress imparted on
the EBV, and thus imparts the user with the ability to control of
the local mechanical environment which drives key cellular
processes. Such control is due to the use and application of
pressure and flow waveforms that replicate native hemodynamics.
[0036] In order to control the local mechanical environment via the
pulsatile perfusion bioreactor of the present invention,
predetermined wall stress values can be programmed and
automatically maintained through a feedback loop that integrates
mechanical and geometrical information obtained through
measurements performed on the EBV by a mechanical property
monitoring system that is a component of the pulsatile perfusion
bioreactor. Thus, as the EBV changes dimensions and/or mechanical
properties as a consequence of the progression of the growth and
remodeling processes, the loading imposed on the EBV by the
pulsatile perfusion bioreactor system can be automatically tuned
such that predetermined stress values are maintained. Thus, the
pulsatile perfusion bioreactor of the present invention is
configured to control and optimize the stimuli-response mechanisms
which underpin vascular tissue growth. The various components of
the pulsatile bioreactor of the present invention are discussed in
more detail below.
Applied Pressure and Flow Waveforms
[0037] Before the pulsatile perfusion bioreactor system of the
present invention can be programmed and used for the culture of an
engineered blood vessel, the pressure and flow waveforms to be
applied during culture to achieve the desired stress or loading
levels must be determined. It is known that the shape, peak,
minimum, and average values of blood pressure and flow vary greatly
amongst various vascular tissues. Similarly, hemodynamic and
geometric differences exist between different mammalian species,
even when comparing similar anatomical locations (e.g., the
ascending aorta). These waveforms are modified by the different
downstream reflections, the relative size of blood to blood vessel,
and most notably the diversity in heart rate. Accordingly, pressure
and flow waveforms often do not have the same shape and cannot be
accurately modeled as simple sine waves. Thus, these hemodynamic
waveforms have been quantified using the mean, fundamental (first
harmonic), and additional harmonic components of a Fourier series
representation. Further, the electro-hydraulic analogy provides a
convenient methodology enabling a translation of periodic
hemodynamic qualities into electrical circuits where Fourier
analysis is commonplace. Here the voltage, current, capacitance,
resistance, and inductance are represented as pressure, flow rate,
compliance, resistance and inertia. The simplicity of this
technique makes it well suited for the practicality of the
laboratory bench as physical structures are represented by pumps,
valves, compliance chambers, and culture media.
[0038] As shown in FIG. 1, the typical pressure (P) and flow (Q)
waveforms for a blood vessel are complex and are not simple sine
waves or steady flows. After the pressure and flow waveforms
similar to those shown in FIG. 1 are determined for the specific
native vessel to be replicated as a EBV in order to achieve desired
stress levels to promote the culture of the EBV in a biomimetic
environment, the waveforms are converted into mathematical
expressions that can be applied to the EBV positioned inside the
pulsatile perfusion bioreactor of the present invention via a
computer interface and specific hardware (e.g., a compliance
chamber, pinch valve, etc.).
[0039] Specifically, the present inventors have taken the pressure
and flow profiles for various types of blood vessels in their
native environment and have then converted those waveforms to
mathematical models via Fourier Transform, where the mathematical
models are then used to recreate the pulsatile flow and pressure
waveforms experienced by a native vessel during the culture of a
EBV in the pulsatile perfusion bioreactor of the present invention.
Such a determination can be based on Womersley's approach, which
uses a periodic pressure gradient to predict the temporal velocity
profile within a vessel. This profile does not follow a constant
parabolic shape throughout the cardiac cycle, can exhibit flow
reversal, and may have a maximum velocity that is not necessarily
at the center of the lumen of the vessel. However, centerline
velocity can be easily measured and can be performed non-invasively
with modern approaches such as vascular Doppler, so the present
inventors have utilized this approach. Further, to calculate other
hemodynamic variables of interest, namely volumetric flow rates,
velocity profiles, and wall shear stresses from the measured
centerline velocity, the present inventors have utilized an inverse
Womersley approach to provide both temporal and spatial blood flow
quantities for various types of blood vessels for which replacement
EBVs can be cultured utilizing the pulsatile perfusion bioreactor
of the present invention.
[0040] As a result of the transformation of the pressure and flow
waveforms into mathematical expressions, multiple waveforms can be
applied to the EBV, resulting in a composite pressure waveform and
a composite flow waveform. Each composite waveform can include a
mean pressure component, a fundamental frequency component (e.g., a
first harmonic frequency component), and additional harmonic
frequency components. While in the past, literature has indicated
that a fundamental frequency component plus four additional
harmonic frequency components are required was required to
accurately replicated the pressure and flow waveforms to which a
native blood vessel is exposed, the present inventors have
surprisingly found that an accurate model of composite pressure and
flow waveforms and be developed utilizing less than four additional
harmonic frequency components. For instance, in one particular
embodiment, the composite pressure and flow waveforms includes a
mean or steady component, a first harmonic frequency component
(also referred to as the fundamental frequency component), and a
second harmonic frequency component. In a further embodiment, the
composite pressure and flow waveforms can include a third harmonic
frequency component. Moreover, although not required, additional
harmonic frequency components can be employed in the composite
pressure and flow waveforms to achieve composite waveforms that
most closely mimic the waveforms to which the native blood vessel
of interest is exposed, resulting in the EBV being exposed to
biomimetic tensile and shear stresses. In other words, it is to be
understood that any suitable number of harmonic frequencies can be
utilized up to an n.sup.th harmonic frequency, where n is a whole
number that is 2 or greater.
[0041] One process for deriving the composite pressure and flow
waveforms that can be programmed into a computer interface is
described in more detail below in Example 1.
Bioreactor Components
[0042] Once the waveforms to be applied to the EBV are determined,
the process for culturing the EBV in the pulsatile perfusion
bioreactor of the present invention can be initiated. Referring to
FIG. 2, in one embodiment of the present invention, the pulsatile
perfusion bioreactor 100 includes a computer interface 101 that
controls a pump system that can include a steady flow pump 102 that
can deliver a mean flow and pressure waveform 103 and a peristaltic
pump 104, which can include multiple pump heads depending on the
number of harmonic frequency components to deliver as part of the
composite pressure and flow waveforms. For instance, as shown in
FIG. 2, the peristaltic pump can include a first pump head 106, a
second pump head 108, and a third pump head 110 to deliver a first
harmonic frequency component 112 (i.e., the fundamental frequency
component), a second harmonic frequency component 114, and,
optionally, a third harmonic frequency component 116. Additional
harmonic frequency components of the composite waveforms can be
incorporated into the pump system via additional pump heads.
[0043] In one particular embodiment of the pulsatile perfusion
bioreactor 100 of the present invention, the computer interface 101
is programmed such that cell culture media is introduced via the
pump system into the lumen of an engineered blood vessel (EBV) 128
being cultured in a bioreactor chamber 126 positioned inside an
incubator 124, such that the EBV 128 is subjected to the composite
pressure waveform and the composite flow waveform from the
programmed mean flow 103 and harmonic frequency waveforms 112, 114,
and 116. The EBV 128 is positioned in the bioreactor chamber 126,
which is filled with cell culture media 130, where the media can be
introduced and replaced via media exchange port 140. In addition,
media is delivered through the proximal end 136 of the EBV 128 in a
pulsatile manner via inlet tubing 118 in the form of the composite
flow waveform discussed above and can then be circulated through
the lumen of the EBV 128 and returned to the pump system via outlet
tubing 119. The composite waveforms discussed above can be applied
to the EBV 128 and monitored and adjusted, along with axial wall
stretch, via a feedback loop as growth and remodeling of the EBV
128 progresses to maintain the desired level of tensile and shear
wall stresses on the EBV. For instance, utilizing measurements
recorded via a mechanical property monitoring system 134, which can
include tensile testing components, a camera, etc. (not shown), a
stepper motor controlled pinch valve 132 located at a distal end
140 of the EBV 128 can be adjusted to control the pressure applied
to the EBV 128 as tracked via a pressure transducer 120 integrated
into the pulsatile perfusion bioreactor 100, while a compliance
chamber 120 can also be used to make adjustments to the pulsatility
of the applied waveforms. The mechanical property monitoring system
134 can also include a force transducer to measure static and
dynamic axial forces. From these forces, a real-time assessment of
the static and dynamic stresses can be calculated. Further, a pair
of electronic linear stages (not shown) can be used to apply static
or dynamic axial stretching to the EBV as desired.
[0044] The aforementioned pulsatile perfusion bioreactor 100 can
successfully culture a EBV 128 over an extend period of time, such
as up to about 10 days, as shown via a comparison of FIGS. 3a and
3b. For instance, FIG. 3a shows a porcine renal artery 128a
cultured for 10 days in the pulsatile perfusion bioreactor of the
present invention prior to administration of phenylephrine to
elicit smooth muscle cell (SMC) contraction. FIG. 3b shows a
porcine renal artery 128b cultured for 10 days in the pulsatile
perfusion bioreactor of the present invention after administration
of phenylephrine to elicit smooth muscle cell (SMC) contraction.
The ability of the porcine renal artery 128b to exhibit SMC
contraction and EC dependent dilations demonstrates that the
pulsatile perfusion bioreactor of the present invention can culture
an EBV and demonstrate cell function afterwards. The present
invention may be better understood with reference to the following
example(s).
EXAMPLE 1
[0045] Example 1 demonstrates the ability to determine the pressure
and flow waveforms for various types of blood vessels in their
native environment, which can then be converted to mathematical
models via Fourier Transform, where the mathematical models can be
used to recreate the pulsatile pressure and flow waveforms to which
a native vessel is exposed during the culture of the EBVs of the
present invention. Various waveform components can be combined to
create composite pressure and flow waveforms to apply to the EBV
via the pump system described above.
Introduction
[0046] In Example 1, the groundwork for recreating native blood
vessel hemodynamics for a EBV undergoing tissue culture in a
pulsatile perfusion bioreactor is achieved by recreating the blood
pressure and centerline flow velocity waveforms described in the
classic and contemporary literature. These waveforms are digitized
and represented as mathematical equations using a Fourier series
reconstruction. The volumetric flow rates, found using an inverse
Womersley approach, are used as the input into a 4-Element
Windkessel electro-hydraulic analogy with best fit parameters that
provide a basis for the design of the culture system components to
match in vivo blood pressures. The time-dependent wall shear
stresses and velocity profiles are calculated and compared from the
literature sources providing groundwork for the identification of
key hemodynamic features enabling intra- and inter-species
comparisons.
Materials and Methods
Pulsatile Hemodynamics
[0047] Arterial hemodynamics are characterized by cyclic
pulsatility of both pressure and flow waveforms, the magnitude and
behavior of which depend on cardiac contractility, the blood vessel
location, and downstream resistances. In contrast, venous system
hemodynamics consist predominantly of steady blood pressure and
flow components. The in vivo, pulsatile, volumetric flow rate q(t)
and wall shear stress .tau..sub.w(t) can easily be calculated when
the temporal velocity profile u(r,t) is known using
q ( t ) = 2 .pi. .intg. 0 r a ru ( r , t ) r and ( 1 ) .tau. w ( t
) = - .mu. .differential. u ( r a , t ) .differential. r . ( 2 )
##EQU00001##
Here r is the radial location within the lumen of the vessel with
fixed inner wall radii r.sub.a and .mu. is the viscosity of blood
assumed to be constant at high shear rates.
[0048] From the momentum balance of Navier-Stokes, the governing
equation for unsteady, axisymmetric laminar flow in a rigid tube,
where gravitational effects are neglected is solved using the
Womersley approach. The non-dimensional Womersley number to relates
pulsatility to viscous effects at that frequency, so that
.alpha..sub.n=r.sub.a(.omega..sub.n.rho./.mu.).sup.1/2 (3)
where .rho. is the density of blood and .omega..sub.n represents
the heartbeat frequency with n=1 the fundamental frequency and
n=2,3 the subsequent harmonics in rad/s.
[0049] Normally the entire velocity profile is unknown and only the
centerline velocity u(0,t) profile is the only value reported
(e.g., from pulsed wave Doppler). The complete velocity profile can
be found from
u ( r , t ) = u s ( 1 - r 2 r a 2 ) + n = 1 3 u n ( t ) ( J 0 ( i 3
/ 2 .alpha. n ) - J 0 ( i 3 / 2 .alpha. n r / r a ) J 0 ( i 3 / 2
.alpha. n ) - 1 ) ( 4 ) ##EQU00002##
where u.sub.s and u.sub.n(t) represent the steady and unsteady
centerline velocities at each harmonic and where J.sub.0 and
J.sub.1 are the Bessel functions of the first kind of zeroth and
first order respectively. The volumetric flow rate can be found
from the centerline velocity using equation (1) and (4)
q ( t ) = .pi. r a 2 ( u s 2 + n = 1 3 u n ( t ) ( i 3 / 2 .alpha.
n J 0 ( i 3 / 2 .alpha. n ) - 2 J 1 ( i 3 / 2 .alpha. n ) i 3 / 2
.alpha. n J 0 ( i 3 / 2 .alpha. n ) - i 3 / 2 .alpha. n ) ) ( 5 )
##EQU00003##
Further, the time dependent wall shear stress at the wall can be
found via
.tau. w ( t ) = - .mu. r a ( - 2 u s + n = 1 3 u n ( t ) ( i 3 / 2
.alpha. n J 1 ( i 3 / 2 .alpha. n ) J 0 ( i 3 / 2 .alpha. n ) - 1 )
) . ( 6 ) ##EQU00004##
[0050] Blood pressure (via catheterization) and flow waveforms are
conveniently represented using a Fourier series expansion so
that
q(t)=.SIGMA..sub.n=0.sup.3M.sub.n.sup.q
cos(.omega..sub.nt+.phi..sub.n.sup.q) (7)
and
p(t)=.SIGMA..sub.n=0.sup.3M.sub.n.sup.p
cos(.omega..sub.nt+.phi..sub.n.sup.p), (8)
where M.sub.n and .phi..sub.n are the magnitude and phase of
pressure or flow waves at each frequency. Of note, blood pressure
and flow have the same .omega..sub.n but are out of phase.
[0051] When volumetric flow is given in the form of equation (7)
instead of the centerline velocity, the wall shear stress can also
be calculated directly using the inverse Womersley approach, so
that
.tau. w ( t ) = .mu. .pi. r a 3 ( 4 M 0 q - n = 1 3 M n q cos (
.omega. n t + .phi. n q ) ( i 3 .alpha. n 2 J 1 ( i 3 / 2 .alpha. n
) i 3 / 2 .alpha. n J 0 ( i 3 / 2 .alpha. n ) - 2 J 1 ( i 3 / 2
.alpha. n ) ) ) ( 9 ) ##EQU00005##
and is sometimes the case in the literature. Equation (9) is
convenient as it allows for a calculation of wall shear stress in a
cultured vessel based on the magnitude of steady and pulsatile flow
channels of the device described herein. These are described in the
following section.
Electrical-Fluid Component Design
[0052] The electro-hydraulic analogy employed by earlier
researchers provides a basis for a lumped parameter estimation to
recreate in-vivo hemodynamics. A pictorial representation of the
electrical circuit with corresponding hydraulic elements is shown
in FIG. 3. Application of Kirchhoff s current (volumetric flow) law
yields two first order, linear, differential equations:
p 1 ( t ) t = q ( t ) C - p 1 ( t ) R 1 C and ( 10 ) p 2 ( t ) t =
R 2 q ( t ) t - R 2 p 2 ( t ) L ( 11 ) ##EQU00006##
where p.sub.1(t) and p.sub.2(t) are the pressures across resistors
R.sub.1 (mmHgs/ml) and R.sub.2 (mmHgs/ml) respectively, C (ml/mmHg)
is the downstream compliance, and L (mmHgs.sup.2/ml) is the
inductance. The volumetric flow rate represents the periodic
displacement of a pump or pumps and is considered a configurable
value in the pulsatile perfusion bioreactor of the present
invention. Using Kirchoff's voltage (pressure) law, a third
governing equation is obtained:
p(t)=p.sub.1(t)+p.sub.2(t) (12)
with p(t) representing the pressure at the vessel culture location.
A practical interpretation of these variables as they pertain to a
physical design is provided in the results section.
[0053] Taking the Laplace transform of equations (10) to (12)
provides a transfer function relating the volumetric flow input
Q(s) to pressure output P(s) in the Laplace domain:
P ( s ) Q ( s ) = R 1 R 2 CLs 2 + ( R 1 L + R 2 L ) s + R 1 R 2 (
sR 1 C + 1 ) ( sL + R 2 ) ( 13 ) ##EQU00007##
The time response of the system described by equation (13) is
simulated using the MATLAB.RTM. (Mathworks, Natick Mass.) function
lsim.
[0054] Resistance, capacitance, and inductance values were found by
minimizing the error e.sub.P between the desired pressure waveform
and the system modeled in (13)
e P = j = 1 S p j - p j m j = 1 S p j ( 14 ) ##EQU00008##
where j is the sample number of S total samples. The MATLAB.RTM.
function fminsearchbnd was used to achieve this minimization with
lower limits of zero for each variable. Defining e.sub.p in this
manner will generate a large error when the desired and modeled
pressures are out of phase.
Results
[0055] Combining the techniques of Fourier analysis and the inverse
Womersley approach, key hemodynamic properties are discovered from
in vivo measurements of centerline velocity. Namely, temporal and
spatial velocity profiles are found and plotted as well as the
temporal volumetric flow and wall shear stress. From this
information, the parameters of a blood vessel culture system can be
designed to adequately recreate pulsatile and steady physiologic
blood-pressure and flow in organ culture using an electro-hydraulic
analogy of the 4-element Windkessel model.
[0056] The results of a Fourier analysis of the pressure waveforms
are shown for a diverse set of 3 blood vessels in Table 1. The
various results pertain to the Human Radial Artery (H-RaA), the
Human Renal Artery (H-ReA), and the Mouse Aorta (M-AoA).
TABLE-US-00001 TABLE 1 Magnitude and phase of blood pressure and
flow for each harmonic frequency of the heart rate for the Human
Radial Artery (H-RaA), Pig Renal Artery (P-ReA), and Mouse Aorta
(M-AoA), as well as the dimensionless Womersley number at each
frequency for the vessel. Heart M.sub.0.sup.p . . . M.sub.3.sup.p
.phi..sub.0.sup.p . . . .phi..sub.3.sup.p M.sub.0.sup.q . . .
M.sub.3.sup.q .phi..sub.0.sup.q . . . .phi..sub.3.sup.q
.alpha..sub.0 . . . .alpha..sub.3 Rate (Hz) (mmHg) (rad) (ml/s)
(rad) (..) H-RaA -- 94.1 -- 0.19 -- -- ID = 2.33 mm 7.87 12.8 2.81
0.05 1.75 1.64 15.7 8.05 -2.05 0.05 -2.30 2.31 23.6 4.14 -0.17 0.04
-1.15 2.83 P-ReA -- 68.3 -- 1.68 -- -- ID = 3.88 mm 7.88 8.86 -2.30
0.34 -2.62 2.76 15.8 6.82 0.72 0.27 0.23 3.90 23.7 3.56 -2.99 0.178
-3.08 4.78 M-AsA -- 97.5 -- 0.21 -- -- ID = 1.20 mm 65.5 16.7 -2.93
0.17 1.83 2.54 131 6.94 -0.74 0.07 -2.80 3.59 196 1.36 0.91 0.04
-2.59 4.39
[0057] The magnitude and phase of each the fundamental and harmonic
frequencies of pressure and flow waveforms are quantified in Table
1 and are shown graphically in FIGS. 5a and 5b for a pig renal
artery (P-ReA). The volumetric flow rates shown in Table 1 are
calculated using the inverse Womersley method with measured flow
velocities and the Fourier Analysis. Specifically, referring to
FIGS. 5a and 5b, the composite hemodynamic pressure and flow
waveforms from the pig renal artery are shown, where, in FIG. 5a,
blood pressure is a measured quantity that is reconstructed using a
Fourier analysis, while in FIG. 5b, volumetric flow rate is either
provided by Doppler or calculated from the centerline velocity as
described. The composite waveforms (dotted lines) in FIG. 5a and
FIG. 5b consist of the mean value (n=0, solid line), fundamental
frequency component (n=1, open circle waveform), and the n=2 (open
square waveform) and n=3 (open diamond waveform) harmonic
frequencies shown in FIG. 5a for pressure and in FIG. 5b for
volumetric flow. These composite waveforms are similar to the
superimposed waveforms shown in FIG. 1. The Reynolds number is a
quantity that relates inertial to viscous effects and is given
by
.eta. = 2 u _ r i .rho. .mu. ( 15 ) ##EQU00009##
and all calculated Reynolds numbers yield laminar flow results even
during peak flow confirming the laminar flow assumption.
[0058] Magnitude M.sub.n and phase .phi..sub.n calculations of the
mean frequency n=0, the fundamental frequency n=1, and the
remaining harmonic frequencies n=2 and n=3 demonstrate the
dominance of the low and zero frequency effects on hemodynamics. Of
note, a very good representation of blood pressure and flow could
be achieved with only the mean, fundamental, and 1 or 2 of the
harmonic frequencies. Low Womersley numbers were shown at lower
frequencies in the smaller blood vessels that velocity profiles
tend towards Poiseuille-type parabolic flow.
[0059] The complete velocity profile across the radius of each
blood vessel (a-c) can be seen in FIGS. 6a-6c, where, specifically,
FIGS. 6a-6c show the velocity profiles (3D map) and measured
centerline velocity (dotted line) for (a) Human Radial Artery, (b)
Pig Renal Artery, (c) and Mouse Aorta. For each sample, the
centerline velocity is the only measured velocity location based on
the digitized literature and superimposed on the figure at r=0. The
temporal and spatial differences in velocity profile are
apparent.
[0060] Turning now to FIGS. 7a-7c, using equation (6) the mean
(solid flat line) and pulsatile (solid parabolic/sinusoidal line)
wall shear stresses (.tau..sub.w) are plotted for (a) Human Radial
Artery, (b) Pig Renal Artery, (c) and Mouse Aorta for 2
seconds.
[0061] The best fit parameters of the 4-element Windkessel
simulation, as configured in FIG. 4, are found in Table 2 and are
set to minimize the difference between the desired and actual
pressure waveforms.
TABLE-US-00002 TABLE 2 Best fit parameters of the 4-element
Windkessel model and the cumulative error for each of the mammalian
blood vessels described in Table 1 R 1 ( mmHg s ml ) ##EQU00010## R
2 ( mmHg s ml ) ##EQU00011## C ( ml mmHg ) ##EQU00012## L ( mmHg s
2 ml ) ##EQU00013## e.sub.p H-RaA 503 392 0.0003 4.39 0.03 H-ReA
39.9 0.64 0.0010 10 0.10 M-AsA 485 0.56 0.0001 0.21 0.05
[0062] FIGS. 8a-8c demonstrate a plot of desired pressure, based on
data obtained from the literature, and the modeling results using
the 4-element Windkessel for each blood pressure. Specifically, the
desired pressure response is shown as a solid line and the
simulated pressure response is shown as open circles pressure
responses using the best fit parameters of the electro-hydraulic
4-element Windkessel model. The desired pressure is reported in the
literature for (a) Human Radial Artery, (b) Pig Renal Artery, (c)
and Mouse Aorta, which also shows a zoomed-in section on one mouse
cardiac cycle.
SUMMARY
[0063] Hemodynamic studies of the last 45 years have provided a
wealth of information that can be used as a baseline to design
modern vascular culture systems. In this Example, contemporary
blood flow studies were digitized and analyzed using a Fourier
transform approach to recreate complex waveforms as mathematical
equations consisting of pulsatile pressure and centerline flow
velocity. An inverse Womersley approach was used to calculate the
velocity profile, volumetric flow, and wall shear stress. A
4-element Windkessel model consisting of 2 resistors, a capacitor,
and an inductor was used as a basis for hardware design using the
electro-hydraulic analogy. The coefficients of the 4-Element
Windkessel were found by minimizing the error between the desired
and simulated blood pressure waveforms.
[0064] As a result of the data collected, the following statements
provide a guideline for the construction of the pulsatile perfusion
bioreactor of the present invention:
[0065] i. The volumetric flowrate q represents the output from a
pump or pumps. The current configuration includes a single steady
flow pump with constant output equal to that of M.sup.q.sub.0 and 3
peristaltic pumps that have a sinusoidal output of magnitude
M.sup.q.sub.1-3 and phase .phi..sup.q.sub.1-3. Each of the
peristaltic pumps would have rotational frequency of
.omega.=n.omega..
[0066] ii. The value of resistors R.sub.1 and R.sub.2 represent the
effect of adding a restriction to flow. For R.sub.1, the most
versatile and biocompatible solution would be to use an
electronically controlled pinch valve. R.sub.2, on the other hand,
must also account for the resistance of the vessel itself so that
the total value is R.sub.2=(dp/dz)/q+R.sub.e where R.sub.e
represents the extra resistance and may take a form similar to that
of R.sub.1.
[0067] iii. The capacitance C is a combination of the compliance of
the culture tubing and a compliance chamber. The tubing compliance
is dependent upon length, diameter, and material stiffness. The
compliance chamber can be assembled with an adjustable volume V of
compressible gas so that C=dV/dp and the relationship between the
volume and pressure for a gas can be found using the ideal gas
law.
[0068] iv. The inductance L accounts for the inertia of the blood
mass and takes the form L=(.rho..DELTA.l)/(.pi.r.sub.i.sup.2).
Since the radius of the vessel remains constant, a shorter or
longer section of tissue may be used to adjust this parameter.
Additionally, the length l of the vessel may also be limited
experimentally so the density of the media can be altered with an
additive to match the required value of inductance to
compensate.
[0069] v. A pressure transducer and flow velocity probe can be used
to monitor hemodynamic waveforms. Simple versions, with limited
risk for contamination, include a manometer and a vascular Doppler
probe.
EXAMPLE 2
[0070] Example 2 demonstrates the ability to culture an EBV in the
pulsatile perfusion bioreactor of the present invention over a 10
day culture period where the EBV was subjected to desired stress
levels via adjustment of the composite pressure and flow waveforms
to which the EBV was exposed, while also maintaining sterility and
viability.
[0071] Pig tissue was obtained fresh from a local abattoir and
dissections were performed immediately following tissue
acquisition. Renal arteries were carefully dissected from the
surrounding tissue and mounted to our perfusion device using 6.0
braided sutures. All processes occurred while submerged in culture
media. The supplemented growth media used in the device consists of
Dulbecco's Modified Eagle's Media with 2% heat inactivated fetal
bovine serum, 2% L-glutamine, 1000 units/L penicillin, and 1000 g/L
streptomycin.
[0072] The capacitance was adjusted by changing the volume of air
in the compliance chamber. The magnitude and phase angle of each of
the channels of the pulsatile pump were adjusted according to Table
2 (ReA). Once the tissue was mounted in the culture chamber, it was
placed inside the incubator with the harsh environment camera and
connected to the supply and return tubing for both the lumen and
reservoir. The LabView program was initiated and the pump motor
started under low-pressure, low-flow conditions to remove bubbles.
Once bubbles were removed, the pressure control was initiated and
culture commenced. A hypertensive culture was also performed for 7
days (not shown) where the magnitude of the steady value of
pressure control was 180 mmHg. Every two days for 10 days the
culture media was exchanged for fresh media.
[0073] At the end of the culture period, vessels were pressurized
to 80 mmHg and viability was assessed using Phenylephrine
(10.sup.-5 M) to elicit smooth muscle contraction and
carbamocholine chloride to induce nitric oxide dependent
vasorelaxation (10.sup.-5 M). Contractility and dilation were
observed for this example. Vessels were removed and prepared for
post-culture analysis.
[0074] These and other modifications and variations to the present
invention may be practiced by those of ordinary skill in the art,
without departing from the spirit and scope of the present
invention, which is more particularly set forth in the appended
claims. In addition, it should be understood the aspects of the
various embodiments may be interchanged both in whole or in part.
Furthermore, those of ordinary skill in the art will appreciate
that the foregoing description is by way of example only, and is
not intended to limit the invention so further described in the
appended claims.
* * * * *